In mountainous environments, topography strongly affects the reflectance due to illumination effects and cast shadows, which introduce errors in land cover classifications. However, topographic correction is not routinely implemented in standard data pre-processing chains (e.g., Landsat Analysis Ready Data), and there is a lack of consensus whether topographic correction is necessary, and if so, how to conduct it. Furthermore, methods that correct simultaneously for atmospheric and topographic effects are becoming available, but they have not been compared directly. Our objects were to investigate (1) the effectiveness of two topographic correction approaches that integrate atmospheric and topographic correction, (2) improvements in classification accuracy when analyzing topographically corrected single-date imagery (14 July 2016 and 2 October 2016), versus a full Landsat time series from 2014 to 2016, and 3) improvements in classification accuracy when including additional terrain information (i.e. topographic slope, elevation, and aspect). We developed a physical based model and compared it with an enhanced C-correction, both of which integrate atmospheric and topographic correction. We compared classification accuracies with and without topographic correction using combinations of single-date imagery, image composites and spectral-temporal metrics generated from the full Landsat time series, and additional terrain information in the Caucasus Mountains. We found that both the enhanced C-correction and the physical model performed very well and largely eliminated the correlation (Pearson’s correlation coefficient r ranges from 0.06 to 0.24) between surface reflectance and illumination condition, but the physical model performed best (r ranges from 0.05 to 0.11). Both image composites, and spectral-temporal metrics generated from corrected imagery, resulted in significantly (p ≤ 0.05) higher classification accuracies and better forest classifications, especially for the mixed forests. Adding terrain information reduced classification error significantly, but not as much as topographic correction. In summary, topographic correction remains necessary, even when analyzing a full Landsat time series and including a digital elevation model in the classification. We recommend that topographic correction should be applied when analyzing Landsat satellite imagery in mountainous region for forest cover classification.